Unsolved Conjectures about Egyptian Fractions

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A unit fraction has numerator 1, as in . An Egyptian fraction is a sum of unit fractions, usually distinct. For example, .

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Erdös and Straus conjectured that always has a solution over integers for .

Sierpinski conjectured that always has a solution over integers for .

All have been verified for the Erdös–Straus conjecture [1], but both are still unsolved problems. The Rhind Papyrus and the Egyptian leather scroll solve many similar problems, so these can be considered among the oldest unsolved mathematical problems.

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Contributed by: Ed Pegg Jr (December 2013)
Open content licensed under CC BY-NC-SA


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Reference

[1] A. Swett, "The Erdos–Strauss Conjecture." (Oct 28, 1999) math.uindy.edu/swett/esc.htm.



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